(CNN) -- The family of a Mississippi mayoral candidate claimed Sunday that he died after being "beaten, dragged and burned," but it's an account a medical examiner disputed, saying "I don't know where that is coming from."

On Wednesday, authorities found Marco McMillian's body near a levee between Sherard and Rena Lara, two unincorporated communities about 15 minutes from Clarksdale. The 34-year-old McMillian had been running for mayor of Clarksdale, a city of about 18,000 people in northwestern Mississippi's Delta region.

His body was "set afire," according to his family, who said they twice met with a coroner.

Coahoma County Medical Examiner Scotty Meredith told CNN that there were "signs of an altercation," but that didn't kill him.

"Beating is not the cause of death," said Meredith, who confirmed he'd met twice with McMillian's family. "He was beaten, but not badly."

The medical examiner added he didn't know how the family came to the conclusion that McMillian was dragged and burned.

The late politician's family, in the statement released through his former campaign manager Jarod Keith, called for "a full and thorough investigation." They said McMillian had told "family and close friends that he was very concerned for his personal safety."

"We feel that this was not a random act of violence, based on the condition of the body when it was found," they said. "Marco, nor anyone, should have their lives end in this manner."

Yet Meredith insisted "this was not a targeted attack."

"No way," the medical examiner said. "This was more of a personal dispute."

The Coahoma County Sheriff's Office announced on Thursday that a suspect, Lawrence Reed, faces a murder charge in the death.

Reed, 22, was found in McMillian's wrecked SUV on Tuesday morning and was taken to a hospital.

McMillian's Facebook page shows a glimpse at a man who was politically ambitious. It includes a picture of McMillian posing with President Barack Obama. His campaign motto: "Moving Clarksdale forward."

McMillian's short biography on Facebook said he had spent much of his career raising money for universities after he graduated from Jackson State with a degree in elementary education. He also received a master's in philanthropy and development from Saint Mary's University of Minnesota.

In 2004, Ebony magazine recognized him as one of the country's top leaders younger than 30. He received the Thurgood Marshall Prestige Award from the Thurgood Marshall College Fund five years later.

And from 2007 to 2011, McMillian was executive director of his fraternity, Phi Beta Sigma, which after his death recalled how he'd "made an incredible difference in his community." He secured the first federal contract to raise awareness about HIV and AIDS among African-Americans for the fraternity and helped it form partnerships with organizations such as the U.S. Marine Corps and the Centers for Disease Control and Prevention in discussing the disease.

Patricia McMillian said that even though media reports since her son's death have labeled him as openly gay, his death likely had nothing to do with his sexual orientation.

Without offering specifics, the family said Sunday that it hoped to share information from the ongoing investigation in order "to dispel speculations surrounding his death."